Questions What is the difference between a discrete random variable and a continuous random variable? What is the sum of the probabilities in a probability distribution? What is an example …

The single or multiplex complexity of its extent is surmised. Overall, the continuous stream of data provided by the Hubble Space Telescope (HST) helps further analysis of stationary ground …

The mean value theorem states : If #f# is is a function defined and continuous on the Inteval #I= [a,b]# and differentiable on the interval # (a,b)#, then there is a value #c in (a,b)# such that

Quantization of any physical quantity is that it can only take some discrete values and not continuous values. Example - Quantization of electric charge means that all charges in nature …

Sep 29, 2014 · There are three types of binary compounds: Type I, a metal of fixed charge and a nonmetal Type II, a metal of variable charge and a nonmetal Type III, two non-metals Type II …

Apr 30, 2018 · An Intuitive "proof": The function is defined for all values #x# with the exception of a discontinuity at #x=0#. Hence, given the restricted domain #x in (0,oo)# the function is well …

Please see below. f (x) = 5-1/x is continuous on the interval [1,4] because the only place it is not continuous is 0 which is not in [1,4]. Therefore, there is a c in [1,4] with f (c) = "average value …

R_f=(-oo,1] f(x)=1-sqrtx , x>=0 D_f=[0,+oo) f is continuous in D_f For xinD_f, f'(x)=-1/(2sqrtx) <0 , if x>0 so f is strictly decreasing in [0,+oo) R_f=f(D_f)=f([0 ...

Since #h (x)# is continuous for #x in [a,b]# and has opposite signs at the limits of the interval, Bolzano's theorem states that there is at least one point in the interval #bar x in (a,b)# such that:

c_1= {1/3 (1+sqrt7),1/3 (1-sqrt7)} c_2=ln (e-1) For the Rolle's theorem question, we have f (x) continuous and differentiable (since all polynomials are differentiable by the power and sum …